Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#11711266 |
| Fitting | C2×#1779 ⋊ D3 |
2324 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 2324 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 18 points:
(4,10,8,7)(5,9)(12,15)(13,17)(16,18);(3,4)(5,8,9,7,6,10)(11,12,13,15,14,16,17,18);(1,2)64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72241506, C2×#72252246, C2×#72252250 |
| maximal normal subgroup of | C2×#72241506, C2×#72252246, C2×#72252250 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,10,8,7)(5,9)(12,15)(13,17)(16,18), (3,4)(5,8,9,7,6,10)(11,12,13,15,14,16,17,18), (1,2));